Mayamalavagowla is the first raga taught to students who learn South Indian Carnatic Music. But I wonder what is the western scale used to represent this Raga ? Why did Carnatic Music system selects this Raga for starting lessons? Is there any advantages or disadvantage with this Raga ?
I will answer the question in the title, Stinkfoot is right, for other questions (why is this the most common beginning raga taught), it is better to ask them separately.
The name we give to the western scale that uses the same notes as the Raga Mayamalavagowla is the double harmonic scale.
In C, it looks like this:
Obviously, a raga is about more than just the notes, so the details of Mayamalavagowla (the order, the importance of the notes, and microtonal inflections) isn't covered by the Double Harmonic Scale which is a term which simply describes the 7 notes that makes the scale (and nothing more). I'm not an expert in this, but I know enough to know that a "raga" includes more information that just the scale itself.
Something to note about this scale is, like the major scale, it is "symettric". The intervals from the fifth to the tonic are a repeat of the intervals from the tonic to the fourth. So C Db E F and G Ab B C are the same pattern repeated.
The most well known melody in the west which uses this scale is probably miserlou, a Greek/Turkish folk melody made famous by dick dale's surf rock version and then by the movie pulp fiction, which used it prominently.
In western music the Double Harmonic scale is not a traditional scale, and when it's used, it's often used to give a "middle eastern feel" to music (in film scores for example, music may use this scale to evoke Arabia). That's probably because this scale is very common in middle eastern music (maqam music), where it is known as maqam hijaz kar, (although even more common is the slightly different maqam hijaz which has a flattened 7th.)
This scale is known as the "Phrygian Dominant Scale" and is very common in both Arabic/Turkish/Persian music (where it is known as maqam hijaz) and Jewish Klezmer music (in Jewish music I'm not sure what it's called, but it's everywhere). Greek folk music uses it a lot too. Again, it is not a traditional "western" scale.